# Using and Converting Units

We use equations to express relationships among physical quantities, represented by algebraic symbols. Each algebraic symbol always denotes both a number and a unit. For example, d might represent a distance of 10 m, t a time of 5 s, and v a speed of 2 m>s.
An equation must always be dimensionally consistent. You can’t add apples and automobiles; two terms may be added or equated only if they have the same units. For example, if a body moving with constant speed v travels a distance d in a time t, these quantities are related by the equation

d = vt

If d is measured in meters, then the product vt must also be expressed in meters. Using the above numbers as an example, we may write

10 m = (2 m/s)(5s)

Topics You May Be Interested In
Uncertainty And Significant Figures Buoyancy
Finding And Using The Center Of Gravity Surface Tension
Bulk Stress And Strain Gravitation And Spherically Symmetric Bodies
Shear Stress And Strain Gravitational Potential Energy
Gases Liquid And Density Summary

Because the unit s in the denominator of m>s cancels, the product has units of meters, as it must. In calculations, units are treated just like algebraic symbol with respect to multiplication and division.

Topics You May Be Interested In
Equilibrium And Elasticity Examples On Gravition
Pressure Gauges The Motion Of Satellites
Surface Tension Spherical Mass Distributions
Gravitation A Point Mass Outside A Spherical Shell
Determining The Value Of G The Gravitational Force Between Spherical Mass Distributions

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